How to Calculate Linear Equations

Linear equations describe the relationship between two or more variables. In a linear equation, all variables are multiplied by constants. There are no exponents other than the implicit first power. Linear equations can be used to determine the value of a variable if the corresponding values of the other variables are known. In coordinate geometry, if two separate points are known, a linear equation can be written expressing the line along which those points lie.

Instructions

Determining Values

1. Isolate the variable for which you wish to solve. For example:

   2a + b + 3c = 5

   If you wish to solve for b, write:

   b = -2a - 3c + 5

2. Substitute values for the known variables. For example, if you know the values of a and c, insert them into the equation:

   a= 1
   c= -3

   b = -2(1) - 3(-3) + 5

3. Solve for the remaining variable. For example:

   b = -2(1) - 3(-3) + 5
   b = -2 + 9 + 5
   b = 12

Determining an Equation from Two Points

1. Subtract the two x-values of your points. For example, if the points are (1, 8) and (5, 0), perform 5 - 1 = 4.

2. Subtract the two y-values of your points. Make sure you do this in the same order you did for the corresponding x values. For example, if you subtracted 1 from 5, you must subtract 8 from 0 to arrive at -8.

3. Divide the difference in y-values by the difference in x-values. For example:

   -8 / 4 = - 2

   This is the slope of your line. Write this down in slope-intercept form ( y = mx + b, where m = the slope). For example, y = -2x + b.

4. Substitute one of the points into the slope-intercept equation. For example, 8 = -2(1) + b. Solve for b.

   8 = -2 + b
   b = 10

   This is your y-intercept. The equation for your line can be written y = mx + b, here y = -2x + 10.

References

• Oklahoma City Community College: Linear Equations
• West Texas A & M University: Graphing Linear Equations